On the distance domination number of bipartite graphs
Doost Ali Mojdeh, Seyed Reza Musawi, E. Nazari · Electronic Journal of Graph Theory and Applications · 2020
A subset D ⊆ V ( G ) is called a k -distance dominating set of G if every vertex in V ( G )- D is within distance k from some vertex of D . The minimum cardinality among all k -distance dominating sets of G is called the k -distance domination number of G . In this note we give upper bounds on the k -distance domination number of a connected bipartite graph, and improve some results have been given like Theorems 2.1 and 2.7 in [Tian and Xu, A note on distance domination of graphs, Australasian Journal of Combinatorics, 43 (2009), 181-190].